Mistake 1: Forgetting the chain rule d/dx(sin(3x)) = 3cos(3x), NOT cos(3x). The inner derivative must be included.

Mistake 2: Power rule for variable exponents d/dx(x^(sin x)) ≠ sin(x) * x^(sin x - 1). Use logarithmic differentiation instead. Correct: x^(sin x) * [cos x * ln x + sin x / x]

Mistake 3: Wrong second derivative in parametric form $d^{2y}$/$dx^2$ ≠ $\frac{d^2y/dt^2}{(d^2x/dt^2)}$. Correct: [d/dt$\frac{dy}{dx}$]/$\frac{dx}{dt}$.

Mistake 4: Domain errors in inverse trig simplification sin^(-1)(sin(2t)) = 2t only when -pi/2 <= 2t <= pi/2. For 2t > pi/2, it equals pi - 2t.

Mistake 5: Forgetting |x| in sec^(-1) derivative d/dx(sec^(-1) x) = $\frac{1}{|x|*sqrt(x^2-1}$), not $\frac{1}{x*sqrt(x^2-1}$). The absolute value matters for negative x.

Mistake 6: Confusing d/dx and d/dt In parametric problems, always clearly track which variable you're differentiating with respect to.